Non Supersingular Elliptic Curves for Public Key Cryptosystems
نویسندگان
چکیده
For public key cryptosystems multiplication on elliptic curves can be used instead of exponentiation in finite fields. One attack to such a system is: embedding the elliptic curve group into the multiplicative group of a finite field via weilpairing; calculating the discrete logarithm on the curve by solving the discrete logarithm in the finite field. This attack can be avoided by constructing curves so that every embedding in a multiplicative group of a finite field requires a field of very large size.
منابع مشابه
Finding More Non-Supersingular Elliptic Curves for Pairing-Based Cryptosystems
Finding suitable non-supersingular elliptic curves for pairing-based cryptosystems becomes an important issue for the modern public-key cryptography after the proposition of id-based encryption scheme and short signature scheme. In previous work different algorithms have been proposed for finding such elliptic curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3, 4, 5}. In this ...
متن کاملEfficient elliptic curve cryptosystems
Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation...
متن کاملDiffie-Hellman type key exchange protocols based on isogenies
In this paper, we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves. The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $, is a straightforward generalization of elliptic curve Diffie-Hellman key exchange. The method uses commutativity of the endomorphism ring $ End(E) $. Then using dual isogenies, we propose...
متن کاملQuantum-Resistant Diffie-Hellman Key Exchange from Supersingular Elliptic Curve Isogenies
Possibility of the emergence of quantum computers in the near future, pose a serious threat against the security of widely-used public key cryptosystems such as RSA or Elliptic Curve Cryptography (ECC). Algorithms involving isogeny computations on supersingular elliptic curves have been shown to be difficult to break, even to quantum computers. Thus, isogeny-based protocols represent promising ...
متن کاملTowards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies
We present new candidates for quantum-resistant public-key cryptosystems based on the conjectured difficulty of finding isogenies between supersingular elliptic curves. The main technical idea in our scheme is that we transmit the images of torsion bases under the isogeny in order to allow the two parties to arrive at a common shared key despite the noncommutativity of the endomorphism ring. Ou...
متن کامل